MathDB
Some points in a circle with 0 and 1 write on them

Source: Mayo Olympiad 2011

October 13, 2020
combinatorics

Problem Statement

Given nn points in a circle, Arnaldo write 0 or 1 in all the points. Bernado can do a operation, he can chosse some point and change its number and the numbers of the points on the right and left side of it. Arnaldo wins if Bernado can´t change all the numbers in the circle to 0, and Bernado wins if he can
a) Show that Bernado can win if n=101n=101 b) Show that Arnaldo wins if n=102n=102